List of top Mathematics Questions on Differentiability asked in JKCET

If $ y=tan^{-1}\left(\frac{2x}{1+3x^{2}}\right)+tan^{-1}\left(\frac{5+x}{1-5x}\right) $ , then $ \frac{dy}{dx}= $

Let the function $ f(x) $ be continuous in the interval $ [a, b] $ and differentiable in $ (a, b) $ . Then there is at least one point $ c $ in $ (a, b) $ at which the tangent to the curve $ y = f (x) $ is parallel to

If tan $ y=\frac{sin\,x+cos\,x}{cos\,x-sin\,x} $ , then $ \frac{dy}{dx}= $

The function $ f (x) = |x-10| $ , $ x $ is real number, is

The derivative of $sin\, x$ with respect to $ cos\text{ }x $ is

Discuss the continuity of the function $ f(x)=\sin 2x-1 $ at the point $ x=0, $ and $ x=\pi $ .

If $ y=x{{e}^{2y}}, $ then find $\frac{ dy}{dx} $ .

Differentiate $ \sin \,\,(\sin \,\,2x). $

If $ \left\{ \begin{matrix} \frac{(1-\cos \,4x)}{{{x}^{2}}}, & if & x<0 \\ a, & if & x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & if & x>0 \\ \end{matrix} \right. $ then $ f(x) $ is continuous at $ x=0, $ for $a = ?$

If $ f(x)={{(1+x)}^{n}}, $ then the value of $ f(0)+f'(0)+\frac{f'\,'(0)}{2!}+.....+\frac{{{f}^{(n)}}(0)}{n!} $ is equal to

Let \(f:R\to R\) be a function such that the third derivative of \(f(x)\) vanishes for all \(x\). If \(f(0)=1,\,f'(2)=4\) and \(f''(1)=2,\) then \(f(x)\) equals to

If $ y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right), $ then $ \frac{dy}{dx} $ is equal to

At $ x=\frac{3}{2} $ the function $ f(x)=\frac{|2x-3|}{2x-3} $ is

Derivative of $ {{\log }_{10}}\,x $ with respect to $ {{x}^{2}} $ is